Strongly indexable graphs

AbstractA (p, q)-graph G = (V, E) is said to be strongly k-indexable if it admits a strong k-indexer viz., an injective function ƒ:V→{0, 1, 2, …, p − 1} such that ƒ(x)+ƒ(y)=ƒ+(xy)ϵ⨍+(E)={k, k + 1, k + 2, …, k + q − 1}.In the terms defined here, k will be omitted if it happens to be unity. We find that a strongly indexable graph has exactly one nontrivial component which is either a star or has a traingle. In any strongly k-indexable graph the minimum point degree is at most 3. Using this fact we show that there are exactly three strongly indexable regular graphs, viz. K2, K3 and K2xK3. If an eulerian (p, q)-graph is strongly indexable then q ϵ 0, 3(mod4)

Discussion On Some Important Topics in Graph Theory

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Study of Some Interesting Topics in the Theory of Graphs

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Series-Parallel Operations with Alpha-Graphs

Among difference vertex labelings of graphs, $\alpha$-labelings are the most restrictive one. A graph is an $\alpha$-graph if it admits an $\alpha$-labeling. In this work, we study a new alternative to construct $\alpha$-graphs using, the well-known, series-parallel operations on smaller $\alpha$-graphs. As an application of the series operation, we show that all members of a subfamily of all trees with maximum degree 4, obtained using vertex amalgamation of copies of the path $P_{11}$, are $\alpha$-graphs. We also show that the one-point union of up to four copies of $K_{n,n}$ is an $\alpha$-graph. In addition we prove that any $\alpha$-graph of order $m$ and size $n$ is an induced subgraph of a graph of order $m+2$ and size $m+n$. Furthermore, we prove that the Cartesian product of the bipartite graph $K_{2,n}$ and the path $P_m$ is an $\alpha$-graph

Some Investigations in the Theory of Graphs

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Some Topics of Special Interest in Graph Theory

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